Investigation of Relaxation Time on Viscoelastic Two-Dimensional Flow Characteristics Using FreeFem++

Abstract

Viscoelastic fluid flow models have shown promising scope in modeling the behavior of many industrial materials such as polymeric materials, microfluidics, biological liquids, gels, plastic melts, and geomaterials. The relaxation time in these models is of great physical significance. In this article, we study the impact of relaxation time on the viscoelastic flow characteristics in a two-dimensional baffled cavity. To the best of authors’ knowledge, relaxation time impact on the chosen flow characteristics in the present context has not been studied and presented in the literature before. The constitutive theory of upper convected Maxwell viscoelastic flow incorporating the viscosity ad relaxation time is taken into consideration. To this account, the flow governing PDEs are derived, and an unsteady variational numerical approach based on classical variational setting is presented. A numerical algorithm based on characteristic Galerkin finite elements method is designed and implemented using the programming language FreeFem++. Computations are carried out and drag and lift forces along with other parameters of interests are calculated. Impact of relaxation time on these flow characteristics are studied and analyzed. The relaxation time $R_f$ is assumed to be in the range of $0\le R_f\le 1\times 10-3.$ The flow simulations are carried out for large Reynolds number in the range of 200 ≤ Re ≤ 5000. In addition to the application of FreeFem++, some new and interesting features of the flow characteristics are presented and discussed.